Finite Group Databasebeta

← #21434723

Subgroups — #21434723

Order 7552.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838015C211yesmaximal, characteristic, complemented
2#16838006C211yesmaximal, characteristic
3#16837801C211yesmaximal, characteristic, complemented
4#16837774C211yesmaximal, characteristic, complemented
5#16837771C211yesmaximal, characteristic, complemented
6#16837647C212yesmaximal, complemented
7#16837630C212yesmaximal, complemented
8#16837499C212yesmaximal, complemented
9#16837493C212yesmaximal, complemented
10#16837359C211yesmaximal, characteristic, complemented
11C59×#490C211yesmaximal, characteristic, complemented
12C2×#11745670C2212yes—
13C2×#11745670C2212yes—
14C2×#11745659C2211yescharacteristic
15C2×C8×D59C2211yescharacteristic
16#14273727C2211yescharacteristic
17#14273722—22no—
18#14273719C2211yescharacteristic
19#14273718—22no—
20#14273708—22no—
21#14273707C2212yes—
22#14273699—22no—
23#14273698C2212yes—
24#14273692C2212yes—
25D4×Dic59C2212yes—
26#14273684C2211yescharacteristic
27#14273660C2212yes—
28#14273658C2212yes—
29#14273652C2212yes—
30#14273652C2212yes—
31#14273637C2211yescharacteristic
32C4×C59⋊C8C2211yescharacteristic
33C8×Dic59C2211yescharacteristic
34#127×C59C2211yescharacteristic
35#125×C59C2211yescharacteristic
36#102×C59C2212yes—
37#102×C59C2212yes—
38#97×C59C2211yescharacteristic
39C2×D4×C59—22no—
40C2×D4×C59C2312yes—
41C2×C22⋊D59—22no—
42C22×Dic59—22no—
43C2×C4×D59C2311yescharacteristic
44C2×Dic118C2312yes—
45C2×C8×C59C2311yescharacteristic
46C2×C8×C59C2311yescharacteristic
47C4⋊C4×C59—22no—
48C4⋊C4×C59C2312yes—
49C42×C59C2311yescharacteristic
50C22⋊Dic59—22no—
51C22⋊Dic59—22no—
52#11745670—24no—
53#11745670—24no—
54(C2×D59)⋊C4—22no—
55(C2×D59)⋊C4D412yes—
56C4⋊Dic59—22no—
57C4⋊Dic59—22no—
58C4⋊Dic59C2312yes—
59Dic59⋊C4—22no—
60Dic59⋊C4—22no—
61Dic59⋊C4D412yes—
62C4×Dic59—22no—
63C4×Dic59C2311yescharacteristic
64C2×C59⋊C8C2311yescharacteristic
65C2×C59⋊C8C2311yescharacteristic
66#11745659—22no—
67C8×D59—22no—
68C23×C59—22no—
69C22×D59C2×D411yescharacteristic
70D4×C59—22no—
71D4×C59—22no—
72D4×C59—82no—
73C2×C4×C59—22no—
74C2×C4×C59C2×D412yes—
75C2×C4×C59C2411yescharacteristic
76C22⋊D59—82no—
77C2×Dic59—22no—
78C2×Dic59—22no—
79C2×Dic59—82no—
80C2×Dic59C2×D412yes—
81C2×Dic59C2×D411yescharacteristic
82C4×D59—21no—
83C4×D59—21no—
84Dic118—22no—
85Dic118—22no—
86C8×C59—21no—
87C8×C59—21no—
88C59⋊C8#4112yes—
89C59⋊C8#4112yes—
90C22×C59—42no—
91C22×C59—42no—
92C22×C59—42no—
93C22×C59C22×D411yescharacteristic
94C2×D59—21no—
95C2×D59—22no—
96C4×C59—22no—
97C4×C59—42no—
98C4×C59C2×#4111yescharacteristic
99C4×C59C2×#4111yescharacteristic
100Dic59—21no—
101Dic59—22no—
102Dic59—42no—
103Dic59—42no—
104#3174—591nomaximal, Sylow
105C2×C59—82no—
106C2×C59#53211yescharacteristic
107C2×C59#57712yes—
108D59—41no—
109#541—591no—
110#540—591no—
111#499—591no—
112#492—591no—
113#491—591no—
114#490D5911yescharacteristic, complemented
115#468—592no—
116#465—592no—
117#440—592no—
118C4×SD16—592no—
119#405—591no—
120C59#317411yescharacteristic, complemented, Sylow
121C2×SD16—592no—
122C2×SD16—592no—
123C2×M16—591no—
124C22×C8—591no—
125C4⋊Q8—591no—
126#127C2×D5911yescharacteristic
127#126—1182no—
128#125—591no—
129#125—1182no—
130#125C2×D5911yescharacteristic
131#123—1182no—
132C22⋊Q8—592no—
133#121—592no—
134#121—1182no—
135C4×Q8—592no—
136C4×D4—592no—
137#117—591no—
138#107—592no—
139#106—592no—
140#103—592no—
141#103—592no—
142#102C2×D5912yes—
143#102C2×D5912yes—
144#97—591no—
145#97C2×D5911yescharacteristic
146C4×C8—591no—
147C4×C8—591no—
148C2×Q8—592no—
149C2×D4—22no—
150C2×D4—1182no—
151C2×D4C22×D5912yes—
152C22×C4—591no—
153C22×C4—1182no—
154SD16—1184no—
155SD16—1184no—
156M16—1182no—
157C2×C8—591no—
158C2×C8—591no—
159C2×C8—1182no—
160C2×C8C22×D5911yescharacteristic
161C2×C8C22×D5911yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—592no—
164C4⋊C4—592no—
165C4⋊C4—1182no—
166C4⋊C4—1182no—
167C4⋊C4—1182no—
168C4⋊C4—1182no—
169C4⋊C4C22×D5912yes—
170C22⋊C4—592no—
171C22⋊C4—1182no—
172C22⋊C4—1182no—
173C22⋊C4—1182no—
174C42—591no—
175C42—1182no—
176C42C22×D5911yescharacteristic
177C23—22no—
178C23—591no—
179Q8—1182no—
180Q8—1182no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—4722no—
185C2×C4—22no—
186C2×C4—592no—
187C2×C4—591no—
188C2×C4—1181no—
189C2×C4—1181no—
190C2×C4—1182no—
191C2×C4—1182no—
192C2×C4—4722no—
193C2×C4D4×D5912yes—
194C2×C4C23×D5911yescharacteristic
195C8—21no—
196C8—21no—
197C8—592no—
198C8—592no—
199C22—42no—
200C22—42no—
201C22—42no—
202C22—1181no—
203C22—1182no—
204C22C2×D4×D5911yescharacteristic
205C4—22no—
206C4—42no—
207C4—1181no—
208C4—1182no—
209C4—2362no—
210C4—2362no—
211C4#41×D5911yescharacteristic
212C4#41×D5911yescharacteristic
213C2—82no—
214C2—2361no—
215C2#1683795111yescharacteristic
216C2#1683821212yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#490C2
socleC22×C59C22×D4
hypercenter#490D59
hypocenterC59#3174
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16838015C2semidirect
3. #16837801C2semidirect
4. #16837774C2semidirect
5. #16837771C2semidirect
6. #16837647C2semidirect
7. #16837630C2semidirect
8. #16837499C2semidirect
9. #16837493C2semidirect
10. #16837359C2semidirect
11. C59×#490C2semidirect
114. #490D59semidirect
120. C59#3174semidirect